A note on a specification test of independence

In a recent paper Zheng (1997a) proposed a new specification test of independence between two random vectors by the kernel method. He showed asymptotic normality under the hypothesis and local alternatives. The present work investigates the asymptotic distribution of the corresponding test statistic under fixed alternatives. In this case asymptotic normality of a standardized statistic is still valid but with a different rate of convergence. Received: January 1999